# Introduction to Operations Research

## What is operations research?

The study of using mathematics to solve business problems. Operations Research, also known as management science, Decision Science, or Operations Analysis. Operations Research is an advanced analytical method to make better decisions. It has a fascinating position with topics like Data Science and Machine Learning. Further, Operations research is used to analyze complex real-world systems to improve or optimize performance.

## Origin and History of Operations Research.

It is believed that Charles Babbage is the father of Operational Research because his research into the cost of transportation and sorting of mail resulted in England’s universal Penny Post in 1840.

The roots of operations research can be traced back many decades when early attempts were made to use a scientific approach in the management of organizations. The name operation research is called early in World War II when a team scientist in the UK applied the scientific techniques to research military operations to win the war. It was used to deploy radars, manage convoys, prioritize bombing missions, and control anti-submarine operations.

These teams of scientists were the first OR teams. When the war ended, there was an interest in applying operations research outside the military.

## The impact of operations research.

We make daily decisions that involve many factors. These factors are often uncertain and forced to make decisions based on our intuition. With operation research, we can better decisions also work efficiently and productively.

Around the world operations research has had an impressive impact on improving the efficiency of numerous organizations. Operations research is often applied in the following areas*(these are few examples)*:

- Military, Defense and Security Applications
- Public Transport
- Health Care
- Education
- Agriculture & Forestry
- Finance, Investment Analysis, Insurance, and Revenue Management
- The Energy Sector
- Bioinformatics
- Cutting & Packing Problems in the Production Industry
- Airline Crew Scheduling
- Sustainability and the Environment
- Materials Handling & Supply Chain Management
- Maritime Transportation and Logistics

A list of few organizations and how much they annually saved by applications of operations research.

- DHL — Optimized the use of marketing resources — $22 million
- HP — product portfolio management — $180 million
- Deere& Company — management of inventories throughout a supply chain — $1 Billion
- MISO — administer the transmission of electricity in 13 states — $700 million
- Samsung Electronics — reduce manufacturing times and inventory levels — $200 million more revenue
- FAA — Manage air traffic flows in severe weather — $200 million
- Taco Bell — Plan employee work schedules at restaurants— $13 million

# Operations Research Modeling Approach

A model is an abstraction of an idealized representation of a real-life problem. Modeling is a real-life situation helps us to study the different behavior of the problem. It ignores irrelevant details and only represents the relevant details. Operation research requires the use of models, which are mathematical representations of the actual systems.

“All models are wrong, but some are useful.” — George Box, a statistician

The phase of model approach for problem-solving in Operations research:

Most academics focus on the Data Collection, Mathematical Model, and Model Solution, bear in mind the fact that the other steps are equally important from a practical perspective. Insufficient attention to these steps has been the reason why operations research has sometimes been mistakenly looked upon as impractical or ineffective in the real world.

## Orientation

In this phase, the focus point is problem orientation. The primary objective of this step is to address the problem and ensure that all team members have a clear picture of the relevant issues. Typically the team meets several times to discuss all of the issues involved and to arrive at a focus on the critical ones. The purpose of the orientation phase is to gain a clear understanding of the problem and how it relates to various operational aspects of the system, as well as to come to a consensus on the project’s primary focus. In addition, the team should also have an appreciation for what (if anything) has been done elsewhere to solve the same (or similar) problem.

## Problem Definition

This phase further refines the proceedings from the orientation phase to the point where there is a clear definition of the problem in terms of its scope and the results. It should not be confused with the orientation phase. The previous phase is much goal-oriented, and this phase is about developing a well-defined statement of the problem.

## Data Collection

With the explosive growth in big data past two years. Operations research teams now frequently find that their biggest data problem is not that too little is available but there is too much data. In this environment, locating the particularly relevant data and identifying the interesting patterns in these data can become an overwhelming task.

## Mathematical Model

After the problem is defined and the data is collected, the next phase is to reformulate this problem in a form that is convenient for analysis. This phase deserves a lot of attention since modeling is a defining characteristic of all operations research projects.

Models or idealized representations are an integral part of everyday life. A few examples model airplanes, portraits, globes, and so on. Mathematical models are also idealized representations, but they are expressed in terms of mathematical symbols and expressions. The mathematical model of a business problem is the system of equations and related mathematical expression that describes the essence of the problem. In the mathematical model of a business problem, real problems normally do not have just a single “right” model.

## Model Solution

The next phase in operations research is to develop a computer-based procedure for deriving solutions to the problem from this model. You might think that this must be the major part of the study, but actually, it is a relatively simple step. In most cases, the standard algorithms of operations research are applied. In applying a specific technique something important to keep in mind. That it is often sufficient to obtain a *good* solution even if it is not guaranteed to be the *best* solution. Operations teams occasionally use only **heuristic procedures**(i.e., intuitively designed procedures that do not guarantee an optimal solution) **to find a good suboptimal solution**. This is most often the case when the time or cost required to find an optimal solution for an adequate model of the problem would be large.

The economist Herbert Simon uses the term “satisficing” to describe this concept — one searches for the optimum but stops along the way when an acceptably good solution has been found.

## Model Validation

This process of testing and improving a model to increase its validity is commonly referred to as **Model validation. **In this phase, a typical error might be discovered that was ignored in the model formulation. The result is a plainly impractical solution, and the model needs to be adjusted before resolving it. This process is repeated till the results are almost certain to be logical and come from a valid system representation.

## Implementation and modeling

After a system is developed for applying the model. The last phase of an operations research study is to implement this system as prescribed by management. This phase is a critical one because it is here, and only here, that the benefits of the study are reaped. The operations research team gives operating management a careful explanation of the new system to be adopted and how it relates to operating realities. If the model is successfully implemented. The operations research team needs to monitor the initial experience and seek to identify any modifications that should be made in the future.

**REFERENCES**

- Hillier, F. S., and G. J. Lieberman,
*Introduction to Operations Research*, McGraw-Hill Publishing Company, New York, NY, 1995. - Taha, H. A.,
*Operations Research*, Prentice-Hall, Upper Saddle River, NJ, 1997.